Out on a limb: Two minute warning

First, let me introduce a new topic header, “Out on a limb.” Again and anon I will utilize this header to indicate I am going to go way beyond my depth (think Marianas Trench) by proposing theoretical vectors which are, at least to my knowledge, new or different. Since I already have ventured thusly in one prior post, on 2011-02-02, I have altered that header in keeping with this new approach.

Now, to once again go where angels fear to tread.

Seems to me that time, per se, gets short shrift in the whole “spacetime” business with which astrophysics busies itself. And in quantum physics, at least the more popular sources that I skim, time seems hardly an issue at all.

In astrophysics, the main concerns of time study appear to be centered on three areas: searching, astronomically, back in time toward the big bang; how time “slows down” at high velocities; and in the question of time travel, though the latter seems more of a populist sideline. In quantum mechanics, time…well, truth be told, I don’t remember seeing it mentioned as a significant factor; however, I fault my literature review more than anything else.

Still, I went so far as to read Stephen Hawking’s A Brief History of Time. In my estimation, it dealt much more with space and matter than with time. In all, physicists seem scads more preoccupied with issues like dark matter, the cause of gravity or superstring theory. Time may be a factor, but it seems almost incidental.

Here’s what I think: time doesn’t exist.

(To be continued.)

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No show

This one just tickles me pink: the electron has mass but has no dimensions.

A model of an atom, showing an electron.

However, this is not what an atom really

looks like, nor is it what an electron looks

like. But it is colorful.

Simply put, electrons do exist. You could, in theory, weigh one, but you couldn’t measure it’s width—or it’s height or depth, for that matter. No skin, no bones, no structure. It’s what’s referred to as a point particle, meaning that it does not have spatial extension, it does not take up (occupy) any space.

See, it's believed that electrons, one of the essential parts of an atom, are an elementary particle. That is, they are as small as the components of matter get. Since they have no component parts that are smaller than themselves—they have no components at all!

As far as I’m concerned, that there is just plenty enough to boggle the mind for one day.

But there’s more.

If you're among my two avid readers, you might recall that electrons, which operate within the realm of quantum mechanics, spin, some one way, some another, but two can never occupy the same quantum spinning state. But think about this: they spin, despite the fact that they have no surface or structure that can actually move one way or another. You’ll remember, from our glance at quantum entanglement and the Pauli Exclusion Principle, that if one of the electrons spins one way the other has to spin opposite. Just think about it: the little devils spin—even though they've got nothin’ to spin with!

How can you not love particle physics?

This is starting to remind me of that ride at Disney, you know, the Haunted Mansion? Spectral dancers spinning but nobody there. Ghostly heads riding along with you.

I’m thinking that maybe quantum physics depends a lot more on a vivid imagination than it does on math skills.

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PI versus TAU

In 1854 Henry David Thoreau published his best known work, Walden. It’s an account of two years of his life spent in a hut near Walden Pond in eastern Massachusetts. Thoreau, a proficient amateur naturalist, spent much of his time observing, and writing about, the daily minutia of the rural woodland and lakeshore where he was living.

Among his writings is the description of a titanic battle in microcosm, an account of a mortal conflict between two species of ants that he watched close up, on his very doorstep. He reports on the fighting much like a war correspondent, describing the fury and devastation with which the tiny combatants attacked one another and the death and destruction that ensued. And all of it hidden among the weedy stems and leafy grasses around his hut.

One notion that he imparts from that experience was that such hidden conflicts are always around us, but only the careful observer will discover them.

I have discovered such a conflict.

Camouflaged by symbols and formulae, obscured by operands and integers, disguised in chalk dust and flat-screen graphics, a gruesome battle is being engaged in the arcane world of mathematics.

On one side are the Pi (π) loyalists, a group dedicated to the preservation of 3.14159… as the primary definition of the linear and spatial relationships in circles. In opposition are the Tau (τ) revolutionaries, equally motivated number fanatics who insist that 6.28318… is the complex integer that would better serve geometricians, trigonometricians and all-round mathematicians throughout the known universe.

I was raised in the Pi camp. The abridged version of Pi, 3.1416, was a mantra taught early and repeated often in the pre-PC primary, secondary and advanced educational forums through which I progressed. There were no circles without Pi. With due reverence I learned that Pi times the diameter (π x d = c) equals the circumference. I was drilled in reciting that Pi times the radius squared (π x r² = A) equals a circle’s near-mystical Area. Even now, “Pi-r-squared” floats unbidden into my mind whenever I encounter circles or circular objects. It resonates in my near-sub-conscious along with other embedded phrases, like “please-and-thank-you” and “green-eggs-and-ham.”

But in the late 19^th century, some French (wouldn’t you know) mathematician suggested that Tau, which is twice Pi (as the brighter among you may have noticed) is actually the more utilitarian number. As if any numbers that have been calculated out more than a hundred million decimal places—and still counting—could be considered utilitarian. That’s why we round off these numbers: because they appear to be infinitely complex and are, technically, irrational numbers. Really, how handy is that?

Still, it is much more common, among the professional mathematicians, even the mercenaries, to use twice the radius rather than the diameter in doing calculations. Diameter is out, radius is in.

Okay, I admit the distinction escapes me, but for some reason it’s significantly more convenient for advanced mathematics, perhaps comparable to flush toilets versus outhouses. Or maybe not. Chopsticks versus forks? Cans versus long necks? Whatever.

The Tauists (pronounced TOW-ists, and not to be confused with philosophical Tauists, pronounced DOW-ists) insist that Pi is imprecise, since it is used to describe other math properties besides circular ones. Piists (pronounced…oh, never mind) rightly point out that Tau is used in physics to describe certain elementary sub-atomic particles of the lepton family, having a mass about 3,490 times that of the electron, and a mean lifetime of 3×10-13 seconds. (A word to the wise: this may be on Friday's quiz.)

Adding to the fog of war is the trend in current mathematics to parse circles not in portions of their circumference, but in portions based on angular sections of the entire circle, called radial arcs, which apparently confuses some students. I call it collateral damage.

It may not seem important, but consider what is at stake: wedding rings and golf cart tires, trash can lids and shirt neck sizing, clothes dryers and piston rings, geo-stationary TV satellites and icing-filled chocolate cookies, shower drain strainers and wristwatch gears, particle accelerating supercolliders and toddlers teething rings, inner tubes and sliced baloney. Circles reach into every part of our lives—and a battle of covert forces will determine who controls them all.

Eh.

It’s still just arithmetic to me. But, as Thoreau said, “…he must be a great calculator indeed who succeeds.” No problemo—my computer came with a great calculator.

Nevertheless, I hope you celebrated, as I did, this past Monday, March 14^th, marking the 22^nd annual Pi Day (3/14, get it?). Here at the RV park the festivities were somewhat subdued. This was just as well. Because, for me, the whole idea of Pi is a personal experience. I opted to observe the Pi holiday in my usual quiet fashion—with a generous radial arc of a bakery-fresh deep-dish pecan beauty that I nuked to medium hot perfection and then topped with a big scoop of some French (wouldn’t you know) vanilla ice cream.

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Grandson's birthday!

Gravity. No, seriously.

Ask yourself this important question:

Where would we be without gravity?

Think about it. Do you realize how difficult it is to clean up spilled beer uh, milk if there is no gravity? Or to sit in a recliner? Or make a left-hand turn at a busy intersection? Or flush a toilet? Or eat pistachios? Or just hang out?

See what I mean? There is—literally—no telling where we’d be without gravity. Because gravity is what keeps us and everything else pinned to the earth, and that everything else includes items like the water we drink and the air we breathe and the burger on the grill.

Gravity is the earth-bound name for a basic natural force called gravitation, the attraction between bodies of mass. The more mass, the more gravitation. Planets, stars, moons, all exert gravitation. So does a baseball, though not enough to have an effect. So do you and me, but again, not so’s you’d notice.

The gravitational force of the moon, and the sun, are what cause the tides in our seas and oceans. Their gravity tugs at our whole planet, but it is the liquid sea that responds in the most obvious fashion.

Gravity is one of the four natural forces that control our physical universe. Besides gravitation, the others are the electromagnetic force, the strong force and the weak force.

Still, despite the best minds being applied to it—and I mean folks like Aristotle, Galileo Galilei, Isaac Newton and Albert Einstein—we’re still not sure exactly what causes gravitation. Einstein’s theory of general relativity suggests that gravitation is a warping of spacetime, an actual inward flux of the fabric of the universe caused by the mass of objects. The moon, therefore, orbits the earth because it is caught in this four-dimensional gravitational dimple, like a marble spiraling around the inside of a serving bowl with the earth at the center.

A simplified diagram of the spacetime warp caused by gravitation.

In real terms, spacetime is drawn in from all directions. In the case

of our moon, its velocity prevents it from falling to earth; actually,

the moon is very gradually moving away from earth.
CLICK THE IMAGE FOR ANIMATION (Image NASA)

Oh-oh. This reminds me of a joke. Hey, it’s a gravity joke, okay?

A tourist, wandering around the charter boat docks in Key West, sees the captain of a dive boat cleaning scuba gear and he shouts out, “Hey, Captain, why is it that divers always fall backward off a boat?”

At which the captain snarls, “’Cause if they fell forward, they’d still be in the blasted boat!”

There’s a ton of minutiae about gravity, lots of esoterica and other tidbits, but I think there is one significant concept that is, perhaps, most important to keep in mind. It seems that gravitation is the main problem between classical physics and quantum physics. Gravitation doesn’t have much of an effect on the sub-atomic particles that are the basic bits and pieces of all matter. That is why the strong nuclear force and the weak nuclear force were proposed, as a way of explaining the structure and behavior of atomic particles.

I still think they could have come up with better names for them.

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Answer to last week's quiz, what is the sun's stellar name? Sol